Optimal power flow for AC-DC networks
Bibliographic record
Abstract
The presence of distributed generators with DC output power and the advancement in power electronics devices have motivated system planners and grid operators to move towards integration of DC microgrids into conventional AC grid. In this paper, we address the optimal power flow (OPF) problem in AC-DC networks. The goal of the AC-DC OPF problem is to jointly minimize the total electricity generation cost of the network and the cost of transferring active power from the AC grid to the DC microgrids. The optimization problem is subject to the power flow constraints, voltage magnitude limits, the limits of the network power lines, and the limits imposed by the power ratings of AC-DC power electronic converters. The formulated AC-DC OPF problem is shown to be nonlinear. We propose an approach to reformulate the AC-DC OPF problem as an equivalent traditional AC OPF problem. Due to the non-convexity of the AC OPF problem, we use convex relaxation techniques and transform the problem to a semidefinite program (SDP). We show that the relaxation gap is zero. That is the optimal solution of the non-convex and the transformed convex problems are equal. Simulation studies are performed on an IEEE 14-bus system connected to two 9-bus DC microgrids. We show that the sufficient condition for the zero relaxation gap is satisfied, and the proposed SDP approach enables us to find the global optimal solution efficiently.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".